It is well known that washing machines are widely used in domestic and the industrial application. According to the arrangement of the inner basket in a washing machine, conventional washing machines can be divided into two types: the vertical type and the horizontal type. Generally, a vertical type of a washing machine includes an inner basket, an outer basket, a agitator, a driving system and a control system. In the vertical type of a washing machine, an inner basket is disposed vertically in the outer basket, and an agitator is installed on an agitator shaft and is disposed on the bottom of the inner basket. The driving system has an output end and an input end. The agitator shaft is connected to the output end of the driving system. During washing, generally the inner basket does not rotate, while the agitator rotates in two opposite directions alternately. The agitator agitates the water inside the inner basket to rotate and realize washing. However, it has been found that there are a few defects in such a type of the existing washing machine. During washing, the impact strength of the water produced by the agitator is relatively weak, cloths are prone to be tangled and it is quite difficult to increase the ratio of washing to cleanness. In order to overcome the above-mentioned defects, a design of a washing machine with a rotating basket has been developed in the washer's manufacturer, wherein the inner basket is not fixed and is kept in the form of a free float. When the agitator rotates, the inner basket creates a counter-action against the impacting force of the water caused by the rotation of the agitator, so as to make the inner basket to rotate in a opposite direction likely to achieve the “rubbing” effect. However, the rubbing effect obtained by such a arrangement is still not satisfactory. Because a driving power is not imparted to the inner basket, the rotation capability of the inner basket is quite little, and the agitator only rotates on the bottom of the inner basket alternately. Thus, the “rubbing” effect obtained by this washing method is not substantially improved, and the problem of tangling cloths can not be solved well. In a horizontal type of a washing machine, two rolling cylinders which rotate in opposite directions are disposed horizontally. They are connected to two driving power sources and rotate in the opposite directions. Although such a type of a washing machine can realize a better “rubbing” effect, its structure is quite complicated and its cost is higher in manufacture. In order to overcome the defects in the existing washing machine, the present invention provides a transmission mechanism for creating dual-directional rotation suitable to be used in a washing machine. Particularly, this transmission mechanism is suitable for a washing machine in a vertical type.